Anúncios
Research Seminar in Probability and Statistics II - #3- Igor Kravchenko, CEMAT-IST - 2020/06/18
28 maio 2020, 12:41 • Isabel Maria Alves Rodrigues
Research Seminar in Probability and Statistics II - #2 - Cláudia Nunes, CEMAT-IST - 28/05/2020
28 maio 2020, 12:33 • Isabel Maria Alves Rodrigues
Quasi-analytical solution of an investment problem with decreasing investment cost due to technological innovations
In this talk we address, in the context of real options, an investment problem with two sources of uncertainty: the price (reflected in the revenue of the firm) and the level of technology. The level of technology impacts in the investment cost, that decreases when there is a technology innovation. The price follows a geometric Brownian motion, whereas the technology innovations are driven by a Poisson process. As a consequence, the investment region may be attained in a continuous way (due to an increase of the price) or in a discontinuous way (due to a sudden decrease of the investment cost).
For this optimal stopping problem no analytical solution is known, and therefore we propose a quasi-analytical method to find an approximated solution that preserves the qualitative features of the exact solution. This method is based on a truncation procedure and we prove that the truncated solution converges to the solution of the original problem.
We provide results for the comparative statics for the investment thresholds. These results show interesting behaviors, particularly, the investment may be postponed or anticipated with the intensity of the technology innovations and with their impact on the investment cost.
(joint work with Carlos Oliveira and Rita Pimentel)
Research Seminar in Probability and Statistics II - #1 - Cancelled due to Covid-19 containment measures
9 março 2020, 11:31 • Isabel Maria Alves Rodrigues
This important measure of congestion can be monitored by using control charts, such as the one found in the seminal work by Bhat and Rao (1972) or more recently in Chen and Zhou (2015).
For all intents and purposes, this paper focus on three control statistics chosen by Morais and Pacheco (2016) for their simplicity, recursive and Markovian character:
- the number of customers left behind in the M/G/1 system by the n-th departing customer;
- the number of customers seen in the GI/M/1 system by the n-th arriving customer;
- the waiting time of the n-th arriving customer to the GI/G/1 system.
Since an upward and a downward shift in the traffic intensity are associated with a deterioration and an improvement (respectively) of the quality of service, the timely detection of these changes is an imperative requirement, hence, begging for the use of ARL-unbiased charts Pignatiello et al. (1995), in the sense that they detect any shifts in the traffic intensity sooner than they trigger a false alarm.
In this paper, we focus on the design of these type of charts for the traffic intensity of the three single server queues mentioned above.
Joint work with Sven Knoth